> when a succession of powers like e.g. a^b^c is written > should this be interpreted as: > 1. (a^b)^c > or as > 2. a^(b^c) > Which a logical reason is there to chose one or the other? > and how about the interpretation of: > a^b^c^d > how to interprete this using brackets?
As a^(b^c), and the latter as a^(b^(c^d)).
As a sort of a rationale for the convention, note that (a^b)^c can be expressed without parentheses, when superscripts are available, as a^(bc).